Standard Library

Categories

Our friend ThCategory is the main theory in this module.

You can specialize a theory by adding more axioms. In this case we can specialize the theory of categories to that of thin category by adding the axiom that two morphisms are equal if they have the same domain and codomain.

thineq := f == g :: Hom(A,B) ⊣ [A::Ob, B::Ob, f::Hom(A,B), g::Hom(A,B)]
GATlab.Stdlib.StdTheories.ThThinCategoryModule
ThThinCategory

The theory of a thin category meaning that if two morphisms have the same domain and codomain they are equal as morphisms. These are equivalent to preorders.

Category Building Blocks

The remaining theories in this module are not necessarily useful, but go to show demonstrate the theory hierarchy can be built up in small increments.